What is the value of a? 9a - 3(a - 6)= -6 a=?

- anonymous

What is the value of a? 9a - 3(a - 6)= -6 a=?

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- anonymous

@mathstudent55

- mathstudent55

In this equation, you first need to simplify the expression and get rid of parentheses.

- mathstudent55

You need to use the distributive property on the left side.

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## More answers

- mathstudent55

|dw:1443652798689:dw|

- mathstudent55

The first step in this equation is to simplify
-3(a - 6)
using the distributive property

- mathstudent55

|dw:1443652952295:dw|

- mathstudent55

I copied the 9a and the = -6 to the next line.
We are only going to work on what is in the box.
|dw:1443653017673:dw|

- mathstudent55

|dw:1443653089656:dw|

- mathstudent55

That was just applying the distributive property.
Now we simplify -3(-6)
What is (-3) * (-6) = ?

- anonymous

18?

- mathstudent55

Correct, since negative times negative is positive.

- mathstudent55

|dw:1443653260886:dw|

- mathstudent55

We simplified the parentheses. Now we need to combine like terms on the left side.
We need to combine the 9a and -3a terms.
What is 9a - 3a = ?

- anonymous

3a^2?

- mathstudent55

No. The exponent only changes when you multiply variables.
Think of a as some unknown thing. It can be the number of books on a shelf, only you don't know it. If I ask you "there are 9 books and I took away 3 books, how many books are left?" What is the answer?

- anonymous

6

- mathstudent55

9 books - 3 books = 6 books
9 bananas - 3 bananas = 6 bananas
9 shirts - 3 shirts = 6 shirts
9a - 3a = 6a

- mathstudent55

You must keep the "a".
9 - 3 = 6 (no numbers here have "a".)
9a - 3a = 6a
If you have 9 "a's" and you take away 3 "a's" you are left with 6 "a's"

- mathstudent55

|dw:1443653672095:dw|

- mathstudent55

Ok so far?

- anonymous

yes

- mathstudent55

Now we have an equation similar tot eh two we saw before.
We need to undo the addition of 18 by subtracting 18 from both sides.
|dw:1443653770531:dw|

- mathstudent55

Since nothing is being added to or subtracted from 6a, we just copy the 6a down.
What is 18 - 18 ?

- anonymous

0

- mathstudent55

|dw:1443653854679:dw|

- mathstudent55

Good.
What is -6 - 18?

- anonymous

-24

- mathstudent55

Correct.
We have:
|dw:1443654066983:dw|

- mathstudent55

"a" is being multiplied by 6.
We want "a" by itself on the left side.
Now can you tell what we still need to do to get "a" by itself?

- anonymous

subtract it by itself?

- anonymous

@mathstudent55

- mathstudent55

a is being multiplied by 6.
To undo a multiplication, you need to do the opposite operation.
What is the opposite operation to a multiplication?

- anonymous

division

- mathstudent55

Correct.
Since "a" is being multiplied by 6, you need to divide it by 6.
Since we need to do the same to both sides of an equation, we divide both sides of the equation by 6.

- mathstudent55

|dw:1443654727026:dw|

- mathstudent55

What is -24/6 ?

- anonymous

-4

- anonymous

and 6/6 is 1

- mathstudent55

Correct & correct.
We have:
|dw:1443655009021:dw|

- mathstudent55

The solution is
a = -4

- anonymous

Thank You! I have 1 more :)

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